Question

Oblicz.
a) log 8+log 125
b) log₇ 19-log₇ ¹⁹/₄₉
c) log 6-log 2-log 3
d) log ⁷/₄-log 14-log125

Wiadomo, że logx=¹/₃ oblicz:
a) log x⁶
b) log ¹/x³
c) log pierwiastek z x
d log ¹/pierwiastek z x do potęgi 3

Proszę o szybką odpowiedź naprawdę ważne

Answer 1

Oblicz.
a) log 8+log 125= log8*125=log 1000=3
log1000=x
10do pot x=1000
10 do potx =10³
x=3

b) log₇ 19-log₇ ¹⁹/₄₉=log₇ 19: ¹⁹/₄₉=log₇ 19*49/19=
=log₇49=log₇7²=2

c) log 6-log 2-log 3=log6:2-log3= log3-log3=0

d) log ⁷/₄-log 14-log125=log⁷/₄:14-log125=
=log⁷/₄*1/14-log125=log1/8-log125=log1/8:125=
=log1/8*1/125=log1/1000=log(1/10)³=log10⁻³=-3

Wiadomo, że logx=¹/₃ oblicz:

a) log x⁶=6logx=6*1/3=2

b) log ¹/x³=log(1/x)³=3log(1/x)=3log(x)⁻¹=
=-3log(x)=-3*1/3=-1

c) log√ x=½logx=1/2*1/3=1/6

d) log ¹/√x³=
=log (¹/√x)³ =
=3log (¹/√x)=3logx(do pot -½)=3*(-½)logx=3*(-½)*⅓=-½

Answer 2

Oblicz.

Korzystam z własności log
log a + log b = log(a*b)
log a - log b = log(a:b)
log a(do potegi 2) = 2log a
oraz korzystam z def. log
log 1000 = 3 , bo 10(podstawa log) do potęgi 3 = 1000

a) log 8+log 125 = log (8*125) = log 1000 =3
b) log₇ 19 - log₇ ¹⁹/₄₉ = log₇ 19 - ( log₇ 19- log₇ 49 ) = log₇ 19 - log₇ 19 + + log₇ 49 = 0 + 2 = 2
bo 7( podstawa log) do potegi 2 = 49

c) log 6-log 2-log 3 = log(2*3) - log 2 - log3 = log2 + log3- log 2 - log 3 = 0

d) log ⁷/₄-log 14-log125= log 7 - log4 - (log7*2) - log(5 do potęgi3) =
= log 7 - log 4 - (log7 + log 2) - 3 log 5=
= log 7 - log 4 - log7 - log 2 - 3 log 5=
= -2log2 - log 2 -3log 5 = -3log 2 -3 log 5 =
= -3( log2 + log5)
= -3( log 2*5)=
= -3*log 10=
= -3*1 = -3 , bo 10(podstawa log)do potęgi 1 = 10( liczba logarytmowana)

Wiadomo, że logx=¹/₃ oblicz:
a) log x⁶ = 6 log x = 6*(¹/₃) = 2
b) log ¹/x³= log 1 - log x³ = 0 - 3 logx = 0 -3*(¹/₃)= -1
c) log pierwiastek z x =( 1/2)*log x = (1/2)*(¹/₃) = 1/6
d)log ¹/pierwiastek z x do potęgi 3 = log 1 - (3/2)*logx= 0 - (3/2)*(¹/₃) = - 1/2

log 1 = 0, bo 10(podstawa log) do potegi 0 = 1( liczba logarytmowana)

Answer 3

Oblicz.
a) log 8+log 125=log (8*125)=log1000=log 10³=3
b) log₇ 19-log₇ ¹⁹/₄₉=log ₇ (19: ¹⁹/₄₉)=log ₇ (19 * 49/19)=log ₇ 49=2
c) log 6-log 2-log 3=log (6: 2)-log 3=log 3-log 3=0
d) log ⁷/₄-log 14-log125=log (⁷/₄ : 14)-log125 = log (1/8)-log125 =
log (1/8:125)= log (1/1000)= log (10⁻³)= -3

Wiadomo, że logx=¹/₃ oblicz:
a) log x⁶ =6 log x=6*1/3=2
b) log ¹/x³=log1- 3logx=0-3*1/3=0-1=-1
c) log√ x =log x do potęgi 1/2= 1/2 log x=1/2 *1/3=1/6
d log ¹/√ x ³=log1- log √ x ³=0- 3 log √ x=-3 logx do potęgi 1/2= -3 *1/2 logx=
-3 * 1/2 *1/3= -1/2